Flavor changing top decays to charm and a Higgs boson with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi><mml:mi>τ</mml:mi></mml:math> at the LHC

We investigate the prospects of discovering the top-quark decay into a charm quark and a Higgs boson ($t\ensuremath{\rightarrow}c{h}^{0}$) in top-quark pair production at the CERN Large Hadron Collider (LHC). A general two-Higgs-doublet model is adopted to study flavor-changing neutral Higgs (FCNH) interactions. We perform a parton-level analysis as well as Monte Carlo simulations using Pythia 8 and Delphes to study the flavor-changing top-quark decay $t\ensuremath{\rightarrow}c{h}^{0}$, followed by the Higgs decaying into ${\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$, with the other top quark decaying to a bottom quark ($b$) and two light jets ($t\ensuremath{\rightarrow}bW\ensuremath{\rightarrow}bjj$). To reduce the physics background to the Higgs signal, only the leptonic decays of tau leptons are considered, ${\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\mu}}^{\ensuremath{\mp}}+{\overline{)E}}_{T}$, where ${\overline{)E}}_{T}$ represents the missing transverse energy from the neutrinos. In order to reconstruct the Higgs boson and top-quark masses as well as to reduce the physics background, the collinear approximation for the highly boosted tau decays is employed. Furthermore, the energy distribution of the charm quark helps set the acceptance criteria used to reduce the background and improve the statistical significance of the signal. We study the discovery potential for the FCNH top decay at the LHC with collider energy $\sqrt{s}=13$ and 14 TeV as well as a future hadron collider with $\sqrt{s}=27\text{ }\text{ }\mathrm{TeV}$. Our analysis suggests that a high-energy LHC at $\sqrt{s}=27\text{ }\text{ }\mathrm{TeV}$ will be able to discover this FCNH signal with an integrated luminosity $\mathcal{L}=3\text{ }\text{ }{\mathrm{ab}}^{\ensuremath{-}1}$ for a branching fraction $\mathcal{B}(t\ensuremath{\rightarrow}c{h}^{0})\ensuremath{\gtrsim}1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, which corresponds to a FCNH coupling $|{\ensuremath{\lambda}}_{tch}|\ensuremath{\gtrsim}0.023$. This FCNH coupling is significantly below the current ATLAS combined upper limit of $|{\ensuremath{\lambda}}_{tch}|=0.064$.